Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing

Juliet Floyd
Boston University, United States of America | jfloyd@bu.edu

Received: 20-December-2018 | Accepted: 3-April-2019 | Published: 30-June-2019
Disputatio [Jun. 2019], Vol. 8, No. 9, pp. 00-00 | DOI: 10.5281/zenodo.3568216
Article | [EN] | Full Text | Statistics | Copyright Notice [es] | Vol. 8 No. 9

How to cite this article:
Floyd, Juliet (2019). «Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing / El argumento diagonal de Wittgenstein: una variación sobre Cantor y Turing». Disputatio. Philosophical Research Bulletin 8, no. 9: pp. 00–00.

Abstract | Turing was a philosopher of logic and mathematics, as well as a mathematician. His work throughout his life owed much to the Cambridge milieu in which he was educated and to which he returned throughout his life. A rich and distinctive tradition discussing how the notion of “common sense” relates to the foundations of logic was being developed during Turing’s undergraduate days, most intensively by Wittgenstein, whose exchanges with Russell, Ramsey, Sraffa, Hardy, Littlewood and others formed part of the backdrop which shaped Turing’s work. Beginning with a Moral Sciences Club talk in 1933, Turing developed an “anthropological” approach to the foundations of logic, influenced by Wittgenstein, in which “common sense” plays a foundational role. This may be seen not only in “On Computable Numbers” (1936/7) and Turing’s dissertation (written 1938, see (1939)), but in his exchanges with Wittgenstein in 1939 and in two later papers, “The Reform of Mathematical Phraseology and Notation” (1944/5) and “Solvable and Unsolvable Problems” (1954).
Keywords |
Common Sense · Formal System · Turing Machine · Ordinary Language · Philosophical Discussion.

El argumento diagonal de Wittgenstein: una variación sobre Cantor y Turing

Resumen | Turing era un filósofo de la lógica y matemática, y también era un matemático. Su trabajo a lo largo de toda su vida estaba muy en deuda con el ambiente de Cambridge en que fue educado y al cual volvió toda su vida. Se desarrolló una tradición rica y distintiva de la noción como el “sentido común” se relaciona con los fundamentos de la lógica durante los días de estudiante de Turing, de manera sumamente intensiva por Wittgenstein. Los intercambios de éste con Russell, Ramsey, Sraffa, Hardy, Littlewood y otros era parte del trasfondo que moldeó el trabajo de Turing. A partir de un discurso en el Moral Sciences Club in 1933, Turing desarrolló un planteamiento “antropológico” a la fundación de la lógica, influenciado por Wittgenstein, en el cual el “sentido común” juega un papel fundacional. Esto se puede no sólo en “On Computable Numbers” (1936/1937) y la disertación de Turing (redactada en 1938, véase (1939)), sino en sus intercambios con Wittgenstein en 1939 y en dos trabajos posterioes, “The Reform of Mathematical Phraseology and Notation” (1944/1945) y “Solvable and Unsolvable Problems” (1954).
Palabras Clave | Sentido Común · Sistemas Formales · Máquina de Turing · Lenguaje Común · Discusión Filosófica.


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